Unit Conversion

Problems

practice

A 20 km long, 8 m wide, two-lane highway is to be paved with a 4 cm thick layer of asphalt. A fleet of three dumptrucks is to be employed, each with an empty mass of 20 metric tons and a carrying capacity of 20 m3. Asphalt with a density of 0.72 g/cm3 will be used. Determine…

the total volume of asphalt needed

the number of dumptruck loads required

the gross mass of each truck

Determine which of the following expressions are dimensionally consistent.

v2 = 2ax

x = vt + ½at3

tan θ =

v

x

Write something else.

Write something completely different.

algebraic

For each of the following problems let a [m/s2], t [s], v [m/s], and x [m].

Determine the SI unit of each of the following quantities.

v2

ax

at2

2

2π√

x

a

Determine which of the following expressions are dimensionally consistent.

v = xt

x = vt

t = vx

x = at + ½at2

x = vt + ½at3

v2 = 2ax2

x =

√

2a

t

t =

√

2x

a

t =

√

v2

ax

tan θ =

x

y

tan θ =

y

x

tan θ =

v

at

Determine the SI units of the constants C1 and C2 so that the following expressions are dimensionally correct.

x = C1 + C2t

x = C1t + ½C2t2

v = C1t + C2t2

x = C1 sin(2πC2t)

v = ½C1e−C2t

In the formula below the symbol U is measured in kgm2/s2 and x stands for length. What are the units of k?

U = ½kx2

In the formula below the symbol T is measured in seconds and ℓ stands for length. What are the units of g?